I can't see below the soil line but are you sure it isn't just turning yellow below the soil line because of a lack of light? Or, maybe it is callousing due to contact with the soil? I see some of that on my plant. Looking at your pic it seems mostly OK. There are a couple yellow spots that might be cause for concern but bright yellowing like that isn't really a sign of rot in my experience. Usually rot has a darker shade but maybe Hylocereus is different. You can try scooping out some of the soil mix to lower the top of the soil for minimal disturbance of the roots. Maybe exposing the lower part of the rootstock will give it a chance to air out and stop the rot if there is any. Or, unpot the whole plant and reposition it a bit higher. Might need a stake to keep it up until the roots resettle. A more radical solution you can try is cutting the rootstock (the green part) above the rot, let it callous, and then try rerooting it. As greenclaws / Gill pointed out, unfortunately, the scion (top cactus called Gynocalycium) doesn't survive without the rootstock. The babies won't survive without a green rootstock. However, there is a darker purple grafted cactus like this one that can survive without the rootstock. If this cactus doesn't survive don't feel too bad about it. These are known to be tricky. They are two very different kinds of cactus grafted together.

Cut the green parts off and start them in a new pot. Let them callus first (days to weeks to months - I have cut cacti before and let them in the air for weeks to maybe a couple of months - they are that succulent) before sticking in any media (perlite works for rooting) - they are fairly easy to do. Check for scale too. They can overwhelm cacti like this and monstrose types (hiding in crevices that are impossible to get to). The greying out parts could be scabbing over from edema or sun scald.

Looks like too much light and not watered often enough. I know you stated whole greenhouse is in a shaded area but maybe where this plant sits, it is getting a few rogue sunrays hitting parts o f the plant directly, in the areas where its turning purple. I had one in a hanging basket, on a shepard hook, parked under the edge of a large silver maple tree canopy. It started getting some direct sun rays coming through gaps in the tree branches and from western slanting sunrays in early fall. It was my 1st Easter cactus and it ended up looking like your does now. Mine didnt survive but if you gave yours about an hour-long soak in some rainwater & moved it around to spot with better overhead shade, I think you’ll be ok.

i dont understand the 4th pic... where it looks like it cut through some sheet rock or ship board with decorative moss above.. but what the heck is below.. and how wet does the media stay... is that something new.. and have the problems started since that was put there??